I'm trying to install PushWoosh into my non-ARC project using Xcode 5.0.2. I'm using the current PushWoosh SDK from GitHub dated January 8, 2014.

My project is not ARC but I added -fobjc-arc to Other Linker Flags and it made no difference. I even tried adding -fobjc-arc to the individual files that are giving me errors using the Targets -> Build Phases -> Compile Sources method and that didn't make a difference either.

The link that you provided looks like the same method that I said I already tried. This is my third or fourth installation of PushWoosh. The previous ones were with your older SDK and Xcode 4.6 and they all worked fine. It's this new SDK and Xcode 5 that is giving the errors.

I have already tried adding the -fobjc-arc compiler flags and that gives me a whole new set of errors.

-fobjc-arc is not a linker flag, but compiler flag.
As an option just add Pushwoosh as project (xcodeproj file) not as a source.
If you add as a source go to the build phases, compile sources phase, select Pushwoosh source, double-click and add "-fobjc-arc" as per instruction here (under important blue section):